Question: In a class of $9$, there are $5$ students who are martial arts masters. If the teacher chooses $2$ students, what is the probability that both of them are martial arts masters?
We can think about this problem as the probability of $2$ events happening. The first event is the teacher choosing one student who is a martial arts master. The second event is the teacher choosing another student who is a martial arts master, given that the teacher already chose someone who is a martial arts master. The probabilty that the teacher will choose someone who is a martial arts master is the number of students who are martial arts masters divided by the total number of students: $\dfrac{5} {9}$ Once the teacher's chosen one student, there are only $8$ left. There's also one fewer student who is a martial arts master, since the teacher isn't going to pick the same student twice. So, the probability that the teacher picks a second student who also is a martial arts master is $\dfrac{4} {8}$ So, the probability of the teacher picking $2$ students such that both of them are martial arts masters is $\dfrac{5}{9}\cdot\dfrac{4}{8} = \dfrac{5}{18}$